Three dimensional model for protein or part of protein structure

ABSTRACT

The invention refers to modular components to be used in the construction of molecular models representing protein structures. More specifically, the invention discloses components representing parts of the protein which do not form elements of secondary structure and parts of elements of secondary structure, as well as their connections, to build models representing the fold of any protein structure, or even models which are proportional to their real size by establishing a given scale. Said models are useful for teaching purposes and for visualizing protein structure during research work in the field.

FIELD OF THE INVENTION

The invention refers to modular components to be used in theconstruction of molecular models representing protein structures. Morespecifically, the invention discloses components representing parts ofelements of the primary and secondary structure, as well as theirconnections, to build models representing the topology of any proteinstructure, whether adopting a scale or not. Said models are useful forteaching purposes and for visualizing protein structure during researchwork in the field.

BACKGROUND OF THE INVENTION

Proteins are biological macromolecules composed of amino acids. Theyvary enormously in size and molecular weight, and may present a few toseveral hundred KDa. When several such molecules are joined to form amacromolecular complex, this may have a molecular weight in the MDaltonrange, forming molecules having hundreds of thousands of atoms.

In order to perform their various tasks within living organisms,proteins must present particular three-dimensional structures. Saidstructures are specific for each protein and are extremely complex atthe atomic level, due to the very size of the molecules and the numberof their constituent atoms.

The understanding of protein structure is therefore a complex task, butbasic to the comprehension of the activity of these molecules within aliving organism.

Proteins are composed of one or more polypeptide chains which, areformed by the successive condensation of the carboxylic (orα-carboxylic) acid group of one amino acid with the amine group ofanother. Amino acid condensation results in the formation of peptide(amide) bonds joining them in a chain which, in principle, may be of anylength.

There are 20 types of natural amino acids found in proteins, which maybe present in any order along the polypeptide chain. The order of aminoacids forming a chain joined by peptide bonds is called the primarystructure or just the amino acid sequence. Amino acids differ from eachother only by the nature of the radical, also known as the side chain.Excluding the side chains, the remainder of the chain is called thebackbone or main chain.

The peptide bond has the characteristics of a partial double bond, thusresulting in rigidity within the peptide unit. Consequently, the peptideunit is effectively planar and the associated dihedral angle ω (definedby the positions of the atoms Cα(i), C(i), N(i+1) and Cα(i+1), where irefers to any amino acid within the polypeptide chain) is fixed close to180° or, more rarely, 0°. As a consequence, the only freely rotatablesingle bonds within the main chain of a polypeptide are the covalentbonds between the nitrogen of any given amino acid and its Cα andbetween Cα and the carbonyl carbon. The dihedral angles linked to thesetwo bonds are called φ and ψ, respectively, and only a few combinationsof these are stereochemically allowed.

If the combination of φ and ψ is systemically repeated along apolypeptide chain, the resulting structure will be a helix. Although alarge number of such helices is theoretically possible, only a verylimited number is found with a significant frequency in nature. The mostimportant helices are the α-helix and the β-sheet strand (or simplyβ-strand), although other helices, such as collagen and polyprolinehelices, 3₁₀ and π-helices, the latter two of which are similar to theα-helix, are also known. All such helices may be characterized by aseries of standard parameters including the number of residues perhelical turn (n), the displacement along the helix axis per residue (d),the pitch of the helix (p=d×n) and the helix radius (r). A negativevalue of n indicates a left-handed helix (one which spiralsanticlockwise when moving away from the observer) and a positive valueof n designates a right-handed helix (one which spirals clockwise whenmoving away from the observer).

When a polypeptide chain folds up into its native three-dimensionalstructure, stretches of the chain, which assume one of these helicalstructures, are known as elements of secondary structures. The mostcommon structures are α-helices and β-strands, mainly because they leadnaturally to the formation of hydrogen bonds. In the case of theα-helix, hydrogen bonds are internal, formed between the carbonyloxygens of residue i and the amino group of residue i+4. In the 3₁₀helix, hydrogen bonds are formed between i and i+3 and, in the π-helix,between i and i+5.

In the β-strands, hydrogen bonds are not internal to the strands, butare rather formed between two strands. Two or more β-strands joined byhydrogen bonds form a β-sheet, while a two-stranded sheet is also knownas a β-ladder.

The regions of proteins that do not form elements of secondary structureare used to connect such elements. They generally have irregularstructures in which the φ and ψ angles do not systemically repeat, beingknown as loops or turns. The most important group of turns are theβ-turns or reverse turns which consist of four residues. Loops may be ofany length.

The full three-dimensional structure of a polypeptide chain, describedby the coordinates of each one of its component atoms, is called itstertiary structure. If a protein has more than one polypeptide chain,then the arrangement of such chains is called its quaternary structure.

The inherent complexity of such structures makes their understandingdifficult, leading to the use of a common simplification when producinga two-dimensional image, photograph or drawing. In general, thestructure is reduced from an all-atom representation to a simplifiedtopological representation, in which cylinders or spirals represent theα-helices (and similar) and β-strands are shown as arrows or strands.Said figures represent the fold of the peptide chain, since theypreserve the correct sequence of secondary structural elements and theirrelative position, without providing atomic details. Theserepresentations greatly clarify the fold and may be used for teachingand literary illustration, being the object of various specific computersoftware such as RIBBONS (Carson, M. (1997), Methods in Enzymology 277,493-505; J. Appl. Cryst. 24, 958), WHATIF (Vriend, G. (1990) J. Mol.Graph. 8, 52), Molscript (Kraulis, P. (1991) J. Appl. Cryst. 24,946-950), Setor (Evans, S. V. (1993) J. Mol. Graph. 11, 134), and PyMol(Delano, W. L. http://pymol.sourceforge.net).

However, a two-dimensional representation is inadequate for theunderstanding of the real relationship between the component parts ofthe structures, the importance of the fold and for comparison betweentopologies. For such purposes, a three-dimensional model would berequired.

Nicholson describes an all-atom representation model for proteinstructures made out of a large number of rigid color-coded components,as disclosed by the patent U.S. Pat. No. 3,841,001. A scale of 1 cm=1 Åis used and leads to huge models which are difficult to handle in thecase of large proteins. The models must also be permanently fixed bymeans of a base and vertical metal rods.

The English company Cochranes commercializes a number of molecularconstruction systems which also use an all-atom representation but aremore flexible in terms of scale. These models suffer from thedisadvantage that they lead to equally large, cumbersome and verycomplex constructions for most applications.

Ruben and Richardson (Biopolymers III, 2313-2318, 1972) disclose modelsusing wires. Built by bending the wire at each Cα atom, they are asimple way to represent a protein structure, but have the disadvantageof requiring special apparatus for wire bending. On the other hand, thepatent U.S. Pat. No. 4,378,218 discloses that it is possible to improveon the method of Ruben and Richardson by means of a constructioncomprising balls and sticks and a fixed scale in which the Cα positionsare joined by cylinders representing pseudo bonds between adjacent Cαatoms.

Similar systems for the construction of models based on the position ofCα atoms, commercialized by an English university company, in whichresidues are color-identified according to their physical properties andthe scale is fixed at 1 cm=2 Å, can be found.

All mentioned models present the disadvantage that they do not escapefrom an explicit atomic representation, albeit simplified in some cases.Furthermore, the use of colors limits the user's choice andrepresentations are not geared to highlighting the three-dimensionalstructure of the proteins, specifically their topology. None of thepreviously described models are similar to the two-dimensionalrepresentations commonly used in the specialized literature to overcomethe problem of structural complexity.

SUMMARY OF THE INVENTION

The present invention solves the problems of the previous art asdescribed above, particularly the complexity and size of all-atom modelsor Cα representations. The simplicity of the models of the inventionallows highlighting specific aspects of each structure by means ofcolors or materials. The flexibility introduced by adopting anadjustable scale (or no scale at all) means that the models are notlimited to the representation of a specific protein structure and canschematically represent a protein fold common to various differentstructures. The parts composing the model of the invention arepreferably made of sufficiently flexible material to accommodate themany distortions commonly observed in the elements of protein secondarystructure.

One of the objects of the present invention is to provide the componentsfor the construction of three-dimensional topological models of proteinstructures.

It is a further object of the present invention to apply the modelsimply for the construction and demonstration of the basic aspects ofprotein structures, such as e.g. regions of protein structures which donot form elements of secondary structure as well as secondary structuressuch as β-sheet strands and their chirality; β-sheets composed of morethan one strand and their chirality; β-sheets forming saddles, barrelsand coiled coils; β-bulges; α-helices; kinks in α-helices.

A further object of the present invention refers to the use of thecomponents for the production of topological models of the proteinstructure of interest, even including quaternary structures andinteraction among proteins, in which the connectivity of the elements ofsecondary structure, their sequence along the primary structure andtheir relative spatial arrangement are preserved, but with noconsideration of scale.

A further object of the invention refers to components for theconstruction of models in scale, wherein said scale is chosen by theuser.

A further object of the invention are kits for the construction ofthree-dimensional models to represent protein structures.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 shows the nine components for the construction of athree-dimensional model according to a preferred embodiment of theinvention: (a) components used for the construction of the body of α-(3₁₀ or π) helices; (b) and (c) used for the terminal portions of thehelices; (d) β-sheet strand body components; (e) arrowhead componentsused to terminate β-sheet strands; (f) connections between elements ofsecondary structure; (g) components representing pseudo hydrogen bonds;and (h) and (i) connections used to improve the mechanical stability ofthe model.

FIG. 2 shows basic elements of the secondary structure according to apreferred embodiment of the invention: (a) α-helice; (b) untwistedβ-strand; (c) twisted β-strand; (d) helical twisted β-strand; (e) kinkedα-helix, such as that induced by proline.

FIG. 3 shows examples of β-sheet architecture built from elementsaccording to a preferred embodiment of the invention: (a) saddle formedby joining right-handed twisted β-strands by pseudo hydrogen bondsfollowing a rectangular hydrogen-bond array (Salemme, F. R., (1983) 42,95-133); (b) rhombohedral array of hydrogen bonds within the same basicarchitecture shown in (b), leading to the induction of a β-barrel(lighter colored elements); (c) two right-handed coiled twistedβ-strands lead to the formation of a coiled-coil structure, in which thestrand axes are helical; (d) β-bulge formed by introducing oneadditional residue into the darker color strand; (e) the pleated natureof the β-sheet can be emphasized by displacing the components inalternately opposite directions perpendicularly to the strand direction(this representation can be readily achieved by joining a series ofβ-strand body components and bending them into a closed circle which isreopened after some time and subsequently by rotating components by 180°with respect to one another, so to form the pleated structure).

FIG. 4 shows a TIM (Triose Phosphate Isomerase) barrel in a (a)perpendicular and (b) parallel view to the axis of the barrel.

FIG. 5 shows a NAD⁺ (Nicotinamide Adenine Dinucleotide) binding domaincomposed of two Rossmann folds which can be distinguished by the use ofcolors, which is also possible for the helix connecting them. TheN-terminal region of the first helix in the sequence and the previousloop (seen at the left of the figure) are shown in lighter colors, sincethey were made up of components of a different color to emphasize theirfunctional importance in NAD⁺ binding, as referring herein to thevarious shades of black.

FIG. 6 shows a fold known as a six-bladed β-propeller in which thefour-stranded β-sheets are shown in different colours, referring hereinto the various shades of black.

FIG. 7 shows the construction known as a right-handed jelly-roll: (a)represents the basic hairpin structure; and (b) represents the samestructure after folding to form the jelly-roll, composed of twofour-stranded anti-parallel β-sheets. In this case, the negative packingangle between the two β-sheets can be readily seen, i. e. the strandstowards the back of the figure are rotated anti-clockwise by about 30°with respect to the strands towards the front part of the figure.

FIG. 8 shows two four-helix bundles: (a) a right-turning bundle with nocross-over connections (RTO) (Presnell, S. R. and Cohen, F. E. (1989)Proc. Natl. Acad. Sci. 86, 6592-6596); and (b) a similar left-turningbundle (LTO). In both cases, the sequence of the helices is color-codedand the transparent plastic strips give better mechanical strength tothe model, according to a preferred embodiment of the invention.

FIG. 9 shows an α/α barrel as seen in cellulase. Once again, thetransparent strips give better mechanical stability to the model.

FIG. 10 shows purine-nucleoside-phosphorylase, a trimeric structure inwhich the three chains are non-covalently linked and shown in differentcolors, referring herein to the various shades of black.

FIG. 11 shows in (a) ribonuclease on the left and porcine ribonucleaseinhibitor on the right and, in (b), a model for the complex between thetwo proteins in which the ribonuclease fits into the central region ofthe inhibitor. This example shows how the model may be used to representprotein-protein interactions.

FIG. 12 shows in (a) similar constructions to those described for FIG. 4which in (b) were built with a-helices represented by spiraledcomponents and β-strands by straighter and planer components, showinganother particular embodiment of the invention.

FIG. 13 shows, as well as 12, the representation of β-strands similar toFIG. 6 by planer and flatter components and with no connectors.

DETAILED DESCRIPTION OF THE INVENTION

The invention refers to three-dimensional topological models torepresent a protein structure or part thereof, which comprises one ormore of the following components:

i) components to represent the regions of proteins not forming elementsof secondary structure and which are used to join components (ii);

ii) components to represent elements of secondary structure. optionallyincluding at least one of the following components:

iii) component for the schematic representation of hydrogen bonds;

iv) reinforcement component for the mechanical stabilization of themodel.

The term “topology” refers to a representation of the three-dimensionalstructure of proteins preserving the order of the elements of secondarystructure along the polypeptide chain(s) and their connections mediatedby non-covalent bonds, but not necessarily with reference to scale.

In a preferred embodiment of the present invention, components (i) areconstituted of pliable material with no memory, i. e. remaining in theestablished position when the force tending to deform it is withdrawn,particularly in the form of wires. In an even more particularembodiment, said wires have an inner covered filament. The inner wirecan be preferably constituted of metal material, such as e. g. copper,and is preferably covered with flexible material, particularly polymericor elastomeric material, such as used e. g. in electrical wires (FIG. 1f).

According to the present invention, components (ii) may present anyshape, such as geometrical forms, strands, wires or spirals. In apreferred embodiment, components (ii) are of at least two typesregarding their shape:

iia) component to represent elements of secondary structure, whereinsaid element being α-helices (or 3₁₀ or π helices);

iib) component to represent elements of secondary structure, whereinsaid element being β-strands;

Preferably, components (iia) are constituted by cylinders (FIG. 1) orspirals (FIG. 12 b), while components (iib) are represented by strands,arrows or flat oblong shapes (FIGS. 1, 12 and 13). In an even moreparticular embodiment, the model is constituted by one single type ofcomponent (iia), which is a cylinder, and a type of component (iib) withflat oblong forms.

According to the present invention, the elements of secondary structureof the proteins may be represented by one single component (ii) or by anumber of said components. Components (ii a) and (ii b) show, in aparticular embodiment, connections for fitting with other equal ordifferent components. Still more particularly, components (ii a) presenttwo fitting connections and components (ii b) present four fittingconnections. According to a particular embodiment, components shouldpresent a female connection at one of their ends and a male connectionat the opposed end (FIGS. 1 a and 1 d), with the latter fitting thefemale connection of the following component, which is preferably of thesame type regarding its shape, allowing to build structures of any size.

Preferably, components (i) fit into the female connections of thecomponents (ii).

According to the present invention, the components (ii) can alsorepresent the orientation of the polypeptide chains. For this purpose,the end components (corresponding to the C-terminal region of theelement of secondary structure) should present some identification.According to a particular embodiment, components (ii) used to identifythe C-terminal region of the chains do not present a male connection,but rather two female connections. The terminal region of the chain isrepresented by a component ending in a non-connected end. The model canalso comprise component complements, with a different shape,particularly triangles or cones, having at least one, preferably twofemale ends, one to fit the end component of the element of secondarystructure and another one to connect the component (i). These triangularor conical complements of components are preferably different forα-helices and β-strands. According to an even more particularembodiment, the models may comprise, instead of different componentsformed by uniting a component and a complement to be fitted, thedifferent components (i) and (ii) presenting a different shape,preferably an arrow form, not presenting the male connection andprovided with an end having a female connection (FIGS. 1 c and 1 e).

Furthermore, the end region of the chains can be represented by usingcolors. In a particular embodiment of the present invention, theC-terminal region of the chain is represented by a red component and theN-terminal region by a blue component (FIGS. 1 a, b and c) or, in caseswhere the N-terminal and/or C-terminal of the chain is not a part of anelement of secondary structure, by means of a component (i) of thedesired color, preferably red for C-terminal and blue for N-terminal.

The model of the present invention may comprise components (ii a) and/or(ii b) presenting different units by means of characteristics which maybe the shape, color and/or material.

The models of the present invention may comprise a third component (iii)for schematic representation of the hydrogen bonds enabling theformation of β-sheets. Component (iii) is constituted by a pliablematerial with no memory which remains in the established position,particularly wires as component (i), of preferably smaller diameter(FIG. 1 g).

Components (iii) are fitted into the sides of components (iib), whichshould then have fitting connections on the sides. Preferably, saidconnections are female connections. Components (i) and (iii)particularly present a slightly smaller diameter than the orifice ofsaid female connections of the ends and sides, respectively. In aparticular embodiment of the invention, components of the body ofβ-strands present a female connection on each side (FIGS. 1 e and 1 d),a pattern which does not correspond exactly to that which is found innature, being used herein as a schematic representation. This isbecause, according to the invention, the models do not present a fixedscale and, since the number of amino acids corresponding to eachcomponent (iib) has not been previously defined, it would be difficultto establish the number of existing bonds. Components (iii) and thecorresponding connections in components (iib) may be present in anyquantity. Furthermore, components (iii) also perform the function toimprove the mechanical stability of the model. Components (iii) arepreferably white.

Furthermore, the model can also comprise at least one, particularly twotypes of reinforcement components providing greater stability to themodel aiding in the construction of particular conformations, but notrepresenting or corresponding, however, to any aspect of the proteinstructure itself, but especially useful in the representation of morecomplex structures.

In a particular embodiment of the present invention, such reinforcementcomponents (iv) are fitted into the connections present in thecomponents as previously described, particularly into the side femaleconnections or by means of orifices at the ends allowing theirintroduction between the male connection of a component and the femaleconnection of the following component, so to interfere as little aspossible in the protein structure (FIGS. 6, 8 and 9). Therefore, saidcomponents are preferably constituted of transparent material which maybe more rigid or more flexible, according to the region of the structureto which it will be connected, particularly polymers.

In a more particular embodiment, the model of the present inventionadditionally comprises the component (iv a) constituted of poorlyflexible polymeric wires or short sticks fitting into femaleconnections, which can still pass through one or more components (FIG. 1i). Components (iv a) may advantageously have their ends changed so to,on one side, facilitate the introduction of connections, at the sametime making it difficult to release components, and, on the other hand,assure it to remain in the desired position and not simply passingthrough other components, especially when the model is handled.Preferably, component (iv a) presents one end in the form of a halfarrowhead and the opposite one flattened.

The model of the present invention can additionally comprise thecomponent (iv b) constituted of flexible polymeric strands presentingorifices at their ends for the passage of male connections (FIG. 1 h) orcomponents (i) and/or (iii).

The components of the model are formed by single parts or by a set ofhollow or solid parts, according to the material used and according toissues related to production. According to a particular embodiment ofthe present invention, the components of this model, particularlycomponents (ii), are molded by polymer injection, with the aim ofobtaining precision in their shapes and connections. However, themodular nature of the models allows for consecutive components,particularly β-strands, to suffer relative rotations with respect to oneanother, so that the chirality of the strands may be appropriatelyrepresented. Connections should be sufficiently adjusted (tight fitting)for these components to keep their relative position even after rotation(FIGS. 2 & 3).

The components of the invention can be constituted by any material, setor mixture of materials, such as e. g. metals, polymers, woods orceramics. One single model can also comprise components produced fromdifferent materials. Components can also present differences such as e.g. in texture, cut, thickness, recesses or grooves, colors ortransparency, having or not the purpose to identify different regions inthe structures. In a particular embodiment, components of the inventionare colored and the colors may be used to distinguish regions of thechain as described above and the reinforcement components aretransparent (FIGS. 2, 5, 6 and 10.) Furthermore, colors can be used torepresent e. g. different protein domains, active sites, structuralmotifs, secondary structures, modified regions or regions withstructural and/or functional interest, to distinguish between loops andturns and for highlighting a given region, among other purposes.

In a particular embodiment of the present invention, components (iib)are constituted by flexible material, but are able to assure that thechirality of the strands is appropriately represented. Furthermore, theydo not have prominences, have an elliptical cross section and recessesor grooves to improve their mechanical properties. These features helpcomponents and structures built from them to be bent and twisted withoutbreaking, so as to enable the representation of the full complexity ofprotein structures.

The present invention is still more advantageous, since the model may beused for representations not necessarily according to any given scale.The branch of mathematics known topology does not include any notion ofscale, thus allowing the same protein structure to be built withdifferent sizes.

For some applications, however, the user may be interested inestablishing a scale, so as to represent the correct relationshipbetween the sizes of the elements of the protein structure, where themodel now includes components with dimensions that are proportional tothat which is found in nature. An example of a scale which may be usedfor the components of the invention is described below: each component(iia) represents a turn of the α-helix (5.6 Å long) and each component(iib) represents a turn of the β-strand (6.3 Å long). The scale can beadjusted according to the user's interests. Each component can representnot one turn, but half turn or alternatively two turns. In the casewhere one component corresponds to a turn of the strand, each component(iib) will correspond to approximately two residues and the sideconnections (one at each side) to a pair of hydrogen bonds from each oneof the two residues.

Since they are preferably pliable, but keep their shape once bent,components (i) may be molded by the user so to represent the real courseof the peptide chain as precisely as required. Said components may be ofany size and represent the exact shape of loops and their positionregarding the elements of secondary structure or can merely representthe connectivity between the elements of secondary structure with noreference to their real shape. Loops of the same size and shape can beused to emphasize e. g. the pseudo-symmetry of a given fold. The presentinvention therefore allows the representation of a particular structureor a particular fold.

According to the present invention, components can therefore be of anysize. Preferably, components (ii) have the same size.

Therefore, the model of the present invention is more versatile andadaptable than the models known in the state of the art. The models arenot necessarily fixed and can be easily assembled and handled. Inprinciple, any protein structure (represented in terms of its elementsof secondary structure) can be built by using an appropriate combinationof the parts described in the invention. They can be used to representprotein regions that do not form elements of secondary structure,secondary, tertiary and quaternary structures of proteins, changes inthese structures and even interactions among proteins. Furthermore,numerous peculiarities of the structures can be represented, such as e.g. those described herein.

Therefore, the model of the present invention can have various purposes,among them we highlight teaching applications, and in aiding in researchin the field and for the illustration of scientific work.

The present invention also refers to kits comprising at least one of thedescribed components, preferably at least one of each of the fourdescribed components i, ii, iii and iv.

Components can be presented as appropriately as possible according tothe user's interest, comprising individual components with equal ordifferent features or a mix of different components.

According to a particular embodiment of the present invention, the kitcomprises components (i) and (ii) with the same features, but allowingfor differences of interest, such as e. g. color, or at least one of theparticular features as described herein.

In an even more preferred embodiment, the kit of the invention comprisesat least:

-   -   120 components (i), present in six colors (red, yellow, blue,        green, black and white), distributed as follows:        -   72 components of 12 cm long, being each a dozen of one            color;        -   18 components of 17 cm long, being each group of three of            one color;        -   12 components of 22 cm long, being each two of one color,            and        -   18 components of 40 cm components, being each three of one            color.    -   455 components (ii) distributed as follows:        -   165 components (iia) divided as follows:            -   110 components representing the body of α-helices, being                50 red components, 20 green, 20 yellow and 20 blue;            -   55 components representing the end regions of α-helices,                being 25 red components, 10 green, 10 yellow and 10                blue;        -   290 components (iib) divided as follows:            -   205 components representing the body of β-strands, being                100 green components, 35 red, 35 yellow and 35 blue.            -   85 components representing the end region of β-strands,                being 40 green components, 15 red, 15 yellow and 15                blue.    -   250 components (iii), all of them white and distributed as        follows:        -   75 components of 2.8 cm long;        -   100 components of 3.3 cm long; and        -   75 components of 3.8 cm long.    -   components (iv):        -   3 meters of the transparent component (iv a); and        -   60 transparent components (iv b) distributed as follows:            -   30 components of 5.5 cm long; and            -   30 components of 8.5 cm long.

The expert in the art will know how to evaluate that the invention maybe embodied in different ways in the light of the information describedherein.

The examples below represent only illustrative and in no way limitativeembodiments, of the invention.

EXAMPLES Example 1 α-Helices, β-Strands and their Common Distortions

This example shows that, by joining the basic components as describedabove, it is possible to form basic structures representing elements ofsecondary structure. Linear β-strands and α-helices, as shown by FIG. 2a and FIG. 2 b, are formed by means of simply joining the relevantparts. A twisted β-strand may be produced by slight rotation of theconsecutive units of the β-strand (FIG. 2 c). So as to correctlyrepresent the right-handed chirality of a β-strand (as measuredconsidering every second residue), the parts should be turned clockwiseas one moves further from the observer along the axis of the helix. Acoiled twisted β-strand (FIG. 2 d) can be initially produced by closingthe strand into a circle so as to induce an arch, then releasing this byway of opening one of the connections and finally by applying the twistas described above for the twisted strand. β-bulges can be generated byincluding an extra strand component in a strand as compared with itspair (FIG. 3 d). A kink in an α-helix, such as caused by a proline, canbe produced by introducing a connection of small flexible wire betweene.g. a plain end helix component and a conical end helix component.Helices of different types (e.g. 3₁₀ and π) can be distinguished fromα-helices in a structure by simply using different colors.

Example 2 β Strands (Saddles, Barrels and Double-Stranded Coiled Coils)

By joining twisted β-strands with components representing pseudohydrogen bonds, it is possible to generate similar structures to thesaddle shown in FIG. 3 a. This structure includes a rectangularhydrogen-bond array as described by Salemme (Salemme, F. R. (1983)Structural Properties of Protein Beta Sheets, Prog. Biophys. Mol. Biol.42, 95-133), which can be either parallel (as shown) or antiparallel. Arhombohedral array, on the other hand, tends to form barrel structures(FIG. 3 b), to be detailed in the examples that follow. This tendency isshown by the lighter elements in the similar structure to the saddle ofFIG. 3 b. Two twisted β-strands can form a coiled coil of β-strandsjoined by hydrogen bonds as shown by FIG. 3 c.

Example 3 A (β/α)₈ Barrel or TIM (Triose-Phosphate-Isomerase)

This example shows one of the most common topologies observed in enzymestructures. Eight parallel β-strands form a barrel structure in whichhydrogen bonds joining the strands are arranged in the form of arhombohedral array. The strands are parallel among themselves andanti-parallel with respect to the eight α-helices located outside thestrands. The rhombohedral disposition of hydrogen bonds causes aninclination of the β-strands relative to the barrel axis. This can becharacterized by the “shear number” of the barrel, describing thedisplacement (in number of residues) along any given strand when a turnof the barrel is completed by moving from strand to strand along thedirection of the hydrogen bonds. This can be appropriately modeled bythe choice of an appropriate scale for the model. If a shear number of 8for an eight-stranded barrel is desired (as shown by FIG. 4), adisplacement of one residue is required when moving from one strand tothe next. This requires the user to choose a scale in which one β-strandcomponent corresponds to one residue. An expert in the art will be ableto find out the numerous alternatives given by the model to the user. Inthis model, helices are represented by conical ended cylinders.

Example 4 NAD⁺ Binding Domain (Composed of Two Rossmann's Folds)

In this example, a NAD⁺ binding domain is shown, as observed e.g. indehydrogenases. A central β-sheet in the form of a saddle is composed ofsix parallel twisted β-strands. This central β-sheet is surrounded byα-helices on both its sides.

The structure is divided into two parts, each one consisting of threeβ-strands and two associated α-helices. These are known as Rossmannfolds and are shown in darker and lighter shades for the N- andC-terminal halves of the structure, respectively (FIG. 5). The helixconnecting both is shown in an intermediary shade of black on the frontright-hand side of the figure (**). The N-terminal region of the firsthelix and the preceding loop were originally highlighted by means ofcomponents of a fourth color to show their importance in NAD⁺ binding(*). In the present black and white representation the N-terminal regionof the α-helix is represented by an intermediary shade of black,together with, on the bottom left of the figure, the small part ofcomponent (i) connected just to one of the β-strands which appears in adarker shade. In this figure, the ends used for the α-helices arestraight, showing an alternative to that which was presented in theprevious example. This example shows clearly how the use of colors canbe advantageous and effectively employed to emphasize biologicallyimportant information.

Example 5 Six Bladed β-Propeller (As Observed in Neuraminidase)

Structures in the form of a β-propeller have internal pseudo symmetry.Various examples are known in nature, including helices with four, six,seven or eight “blades”. The blades of the structures of FIG. 6 comprisefour anti-parallel β-strands. The example shows that said strandsforming the β-sheet do not need to be the same length. This six-bladedconfiguration corresponds to that observed in neuraminidase and wasoriginally built by components with six different colors, hereinrepresented by light and dark shades, clarifying the pseudo symmetry.

Since there are no hydrogen bonds passing from one β-sheet to another,as they are effectively independent, the final structure may be lessrigid than desired, which is overcome in this example by the use of thetransparent component (iv a) linking nearby blades, which merely servesas a mechanical reinforcement to the structure. These connections arepossible due to the advantage that, in an open β-sheet (not forming abarrel) or a β-sheet having strands with different lengths, some of theside connections will necessarily not be used to form pseudo hydrogenbonds.

Example 6 Four-Helix Bundle

48 topologies are known for four-helix bundles (Presnell, S. R. & Cohen,F. E. (1989) Proc. Natl. Acad. Sci. 86, 6592-6596). Six of them areconsidered as fully anti-parallel, since each of the four helicespresents two anti-parallel neighbors. FIG. 8 shows two of thesebundles—FIG. 8 a shows a right-turning bundle with topology RTO and FIG.8 b shows a left-turning one of topology LTO. In this example, differentshades of gray represent the helix sequence along the polypeptide chain,also emphasized by the representation of terminal regions of the helicesby a component in the form of an arrow or cone, a pattern which couldalso be easily represented e.g. by the use of colored components. Thefigure was originally built by components with different colors, witheach one of the four a-helices being of one color, from blue to red,following a rainbow-based color scale, from the N-terminal to theC-terminal region. The same pattern was used for the structures shown ina and b, so as to highlight the differences in their topologies.

An expert in the art knows that there are preferential packing anglesbetween α-helices in protein structures, including helix bundles. Inclassic bundles, this angle is about +20° and can be easily establishedwhile assembling the model by bending the components (i) which form theconnections between helices.

Since α-proteins have few or no β-sheets, the corresponding model doesnot benefit from the mechanical stability introduced by the pseudohydrogen bonds, resulting in less rigidity than required. Mechanicalstability can be reinforced by components (iv b) positioned betweenhelices. Transparency is again preferred so that these components, notrepresenting aspects of the protein per se, become less evident in thefinal model. FIG. 9 shows another example of the use of said componentsfor the structure of an (α/α)₆ barrel which also possesses no β-sheet.

Example 7 Jelly-Roll

A jelly-roll is formed by twisting a hairpin structure composed ofβ-strands around the external side of a barrel. This example, as shownby FIG. 7, shows the dynamic use of the model. The flexibility ofconnections between the elements of secondary structure (loops andturns) and the simplicity of the model assure that structures can beassembled by the teacher or students in a classroom, in an entertainingand interactive way, so that the students can easily perceive theformation of more complex structures from basic elements.

Example 8 Purine Nucleoside Phosphorilase

Oligomeric proteins are composed of more than one polypeptide chain. Asan example, Purine Nucleoside Phosphorilase is an enzyme of the purinesalvage pathway, which is active in the form of a trimer. In FIG. 10,each of the enzyme subunits is highlighted by using a different shade ofblack. Said shades correspond to the different colors as used in theoriginal model. This example shows the potential of the invention tobuild oligomeric protein structures. When required, components (iv) maybe used to join the various chains of an oligomeric protein.

Example 9 Ribonuclease and its Porcine Inhibitor

The models of the invention can also be used to easily show theimportance of shape complementarity during the phenomenon of molecularrecognition. FIG. 11 shows the structures of ribonuclease and itsporcine inhibitor separately (FIG. 11 a) and in the form of ahypothetical complex (FIG. 11 b). In the latter case, ribonuclease fitsinto the central cavity present in the structure of the inhibitor,demonstrating the complementarity between the two structures. Saidcomplementarity is one of the bases for the biological action ofproteins and its understanding is basic for the full comprehension ofbiological phenomena at the molecular level. Used as such, the inventionfacilitates the teaching of this concept, thus highlighting itspedagogical use.

1-47. (canceled)
 48. A non-simile three-dimensional topological model torepresent a protein structure or a part of a protein structure,comprising: at least one of (i) components to represent regions ofproteins not forming elements of secondary structure and which are usedto join components (ii); (ii) components to represent elements ofsecondary structure; (iii) component for the schematic representation ofhydrogen bonds; and (iv) reinforcement component for the mechanicalstabilization of the model, wherein the components (i) and (ii) arerelatively joined to each other by the same type of junction.
 49. Themodel according to claim 48, wherein the components (ii) include atleast one of (ii a) component to represent elements of secondarystructure, the element being α-helices (or 3₁₀ or π helices), and (ii b)component to represent elements of secondary structure, the elementbeing β-strands, and the (iv) reinforcement component includes at leastone of (iv a) reinforcement component for the mechanical stabilizationof the model in the form of at least one of wires or small rods, and (ivb) reinforcement component for the mechanical stabilization of the modelin the form of strips.
 50. The model according to claim 49, wherein thecomponents (i) and (iii) present an elongated form.
 51. The modelaccording to claim 49, wherein the component (ii a) presents at leastone of a cylindrical or spiral form.
 52. The model according to claim49, wherein the component (ii b) presents a flattened elongated form.53. The model according to claim 52, wherein the component (ii b)presents an elliptical cross-section and grooves on the surface.
 54. Themodel according to claim 49, wherein the components are formed by one ofa single piece or a set of hollow or solid pieces.
 55. The modelaccording to claim 49, wherein structural elements of the proteins areconstituted by one or more components.
 56. The model according to claim49, wherein the components (ii a) and (ii b) present connections forfitting with other equal or different components.
 57. The modelaccording to claim 56, wherein the components (ii a) present two fittingconnections and the components (ii b) present four fitting connections.58. The model according to claim 56, wherein the components (ii a) and(ii b) present a female fitting connection at one end.
 59. The modelaccording to claim 58, wherein the components (ii a) and (ii b) of themodel present one of a male or female fitting connection at the otherend.
 60. The model according to claim 49, wherein the model comprises atleast one of components (ii a) and (ii b) presenting different units bymeans of features including at least one of their form, color, ormaterial.
 61. The model according to claim 60, wherein the modelcomprises at least one of components (ii a) and (ii b) in the form of atleast one of an arrow or cone.
 62. The model according to claim 61,wherein at least one of the components (ii a) and (ii b) present afemale fitting connection at each end.
 63. The model according to claim60, wherein at least one of the components (ii a) and (ii b) are formedby a component of the model and a complement.
 64. The model according toclaim 56, wherein at least one of the components (ii a) and (ii b)present side connections for fitting to other components of the model.65. The model according to claim 64, wherein the components (ii b)present at least one female connection at each side to be fitted to thecomponents (iii).
 66. The model according to claim 48, wherein thecomponents (i) are fitted to female connections at the ends of thecomponents (ii).
 67. The model according to claim 48, wherein thecomponents (iii) are fitted to female connections on the sides of thecomponents (ii).
 68. The model according to claim 48, wherein thecomponents (i) and (iii) present smaller diameter than a hole of thefemale connections of the ends and sides, respectively.
 69. The modelaccording to claim 49, wherein the model comprises at least one ofcomponents (i) and (iii) in the form of wires.
 70. The model accordingto claim 49, wherein the model comprises components (iv a) in the formof at least one of wires or small rods.
 71. The model according to claim70, wherein the model comprises components (iv a) with an end in theform of a half arrowhead and the other opposite end flat.
 72. The modelaccording to claim 49, wherein the model comprises components (iv b) inthe form of strips.
 73. The model according to claim 72, wherein themodel comprises components (iv b) presenting holes at their ends. 74.The model according to claim 49, wherein the components (iv a) areconnected to side female fitting connections of the components (ii b).75. The model according to claim 49, wherein the components (iv b) areconnected to at least one of male connections of the components (ii) orto components (i).
 76. The model according to claim 49, wherein thecomponents are constituted by at least one of wood, polymers, metals, orceramics.
 77. The model according to claim 76, wherein at least one ofthe components (i) and (iii) is a flexible wire with no memory, whichremains in a given position after removing a force tending to deform it.78. The model according to claim 77, wherein at least one of thecomponents (i) or (iii) are constituted of an inner material filamentcovered with polymeric material.
 79. The model according to claim 76,wherein the components (ii) and (iv) are constituted of a polymericmaterial.
 80. The model according to claim 79, wherein the components(ii b) and (iv b) are constituted of flexible polymeric material. 81.The model according to claim 49, wherein the model comprises componentsof different colors.
 82. The model according to claim 81, wherein themodel comprises components (ii) of at least two different colorsincluding blue and red.
 83. The model according to claim 81, wherein themodel comprises components (i) of the same color as components (ii). 84.The model according to claim 81, wherein the model comprises components(iii) in a white color.
 85. The model according to claim 81, wherein themodel comprises transparent components (iv).
 86. The model according toclaim 49, wherein the model comprises components with measurementsrepresenting a proportional scale to that which is found in nature. 87.The model according to claim 86, wherein the model comprises componentsrepresenting a given number of residues in a peptide chain.
 88. Themodel according to claim 49, wherein the model comprises components (iia) and (ii b) with the same length.
 89. The model according to claim 48,wherein the components (i) and (ii) are relatively joined to each otherby a circular cross-sectional male-female (pin-into-hole) connection.90. A kit to represent a three-dimensional model for a protein structureor a part of a protein structure, comprising: at least one of (i)components to represent regions of proteins not forming elements ofsecondary structure and which are used to join components (ii); (ii)components to represent elements of secondary structure, including atleast one of (ii a) component to represent elements of secondarystructure, the element being α-helices (or 3₁₀ or π helices), and (ii b)component to represent elements of secondary structure, the elementbeing β-strands; (iii) component for the schematic representation ofhydrogen bonds; and (iv) reinforcement component for the mechanicalstabilization of the model, including at least one of (iv a)reinforcement component for the mechanical stabilization of the model inthe form of at least one of wires or small rods, and (iv b)reinforcement component for the mechanical stabilization of the model inthe form of strips, wherein the components (i) and (ii) are relativelyjoined to each other by the same type of junction.
 91. The kit accordingto claim 90, which comprises at least: components (i) distributed as 72components of 12 cm long, 18 components of 17 cm long, 12 components of22 cm long, and 18 components of 40 cm long; components (ii) distributedas 165 components (ii a) divided as 110 components representing the bodyof α-helices, and 55 components representing the end regions ofα-helices, and components (ii b) divided as 205 components representingthe body of β-strands, and 85 components representing the end region ofβ-strands; components (iii) distributed as 75 components of 2.8 cm long,100 components of 3.3 cm long, and 75 components of 3.8 cm long; andcomponents (iv) including 3 meters of the component (iv a), and 60components (iv b) distributed as 30 components of 5.5 cm long, and 30components of 8.5 cm long.
 92. The kit according to claim 91 whichcomprises at least: components (i) present in red, yellow, blue, green,black and white distributed as 72 components of 12 cm long with eachdozen of one color, 18 components of 17 cm long with each group of threeof one color, 12 components of 22 cm long with each two of one color,and 18 components of 40 cm long with each three of one color; components(ii) distributed as components (ii a) divided as 110 componentsrepresenting the body of α-helices with 50 red components, 20 greencomponents, 20 yellow components and 20 blue components, and 55components representing the end regions of α-helices distributed as 25red components, 10 green components, 10 yellow components, and 10 bluecomponents, and components (ii b) divided as 205 components representingthe body of β-strands distributed as 100 green components, 35 redcomponents, 35 yellow components and 35 blue components, and 85components representing the end region of β-strands distributed as 40green components, 15 red components, 15 yellow components, and 15 bluecomponents; components (iii), all of them white and distributed as 75components of 2.8 cm long, 100 components of 3.3 cm long, and 75components of 3.8 cm long; and components (iv) including 3 meters of atransparent component (iv a) and 60 transparent components (iv b)distributed as 30 components of 5.5 cm long and 30 components of 8.5 cmlong.